Research On The Consistency Of Fuzzy Complementary Judgment Matrix And Decision-making Method Based On Partially Ordered Set

As an effective comprehensive evaluation method in multi-attribute decision making,fuzzy complementary judgment matrix has been widely used in multi-attribute group decision making and various comprehensive evaluation models to obtain index weights.By expounding the current research situation at home and abroad,the paper finds out the defects and deficiencies of the existing decision methods in consistency adjustment and application of fuzzy complementary judgment matrix,such as the consistency adjustment method of fuzzy complementary judgment matrix has the problem that the inspection effect cannot be guaranteed;The group decision making method based on the consistency of fuzzy complementary judgment matrix has poor robustness?the traditional fuzzy complementary judgment matrix group aggregation method is unable to solve the problem of incomplete fuzzy complementary judgment matrix and the difficulty of weighting comprehensive evaluation method.Therefore,based on the theory of multi-attribute decisionmaking,the paper introduces the theory of partial ordered sets,optimization research is carried out around the consistency of complementary judgment matrix and the problems existing in decision making method.The main research contents and results are as follows:(1)Test of fuzzy complementary judgment matrix based on partial ordered sets and improved statement theorem are given.The insufficiency of domestic and foreign methods of consistency inspection and adjustment is found,looking for the coincidence point between the consistency definition of complementary judgment matrix and the theory of partial ordered sets.By using the method of equivalence proof,a theorem for verifying the consistency of complementary judgment matrices based on partial ordered sets is proposed.lt is an improvement of the stability of the existing consistency test method of complementary judgment matrix;The second is the improvement method of the consistency of complementary judgment matrix.The concordant point of consistency definition of partial ordered set theory,cut set theory and complementary judgment matrix is sought,a theorem to improve the incongruent complementary judgment matrix is proposed by using the method of equivalence proof.(2)The consistency test and ordering theorem of incomplete fuzzy complementary judgment matrix based on partial ordered sets are proposed.To sort out the ranking methods of incomplete complementary judgment matrix at home and abroad,looking for the coincidence point between the theory of partial ordered sets and the consistency definition of incomplete complementary judgment matrix,The consistency theorem and sorting method of incomplete complementary judgment matrix are proposed by using the method of equivalence proof.It is the improvement of consistency level of incomplete complementary judgment matrix and the stability of ranking results.(3)A partial ordered set representation theorem of group decision making for most rules based on the consistency of fuzzy complementary judgments is proposed and a group decision making model based on the consistency of incomplete fuzzy complementary judgments is established.On the basis of defining relevant concepts,two kinds of group decision making methods based on the consistency of fuzzy complementary judgment matrix are presented by using the theory of partial ordered set and the proof of equivalence theorem.(4)A partial ordered set representation model of comprehensive evaluation based on the consistency of fuzzy complementary judgment matrix is established.Based on the multi-attribute decision making method,aiming at the fuzzy complementary judgment matrix weighting dispute empowerment controversy,a linear weighting method based on partial ordered sets with unknown weights is presented to solve the problem that the linear weighting method is difficult to assign weight.